Chen, Jian-Zhong; Shi, Zhong-Ke Solution of 2D shallow water equations by genuinely multidimensional semi-discrete central scheme. (English) Zbl 1203.76021 J. Hydrodyn., Ser. B 18, No. 4, 436-442 (2006). Summary: A numerical method for solving the two-dimensional shallow water equations was presented. This method was based on the third-order genuinely multidimensional semi-discrete central scheme for spatial discretization and the optimal third-order Strong Stability Preserving (SSP) Runge-Kutta method for time integration. The third-order compact Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction was adopted to guarantee the non-oscillatory behavior of the presented scheme and improve the resolution. Two kinds of source terms were considered in this work. They were evaluated using different approaches. The resulting scheme does not require Riemann solvers or characteristic decomposition, hence it retains all the attractive features of central schemes such as simplicity and high resolution. To evaluate the performance of the presented scheme, several numerical examples were tested. The results demonstrate that our method is efficient, stable and robust. Cited in 2 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M12 Finite volume methods applied to problems in fluid mechanics Keywords:2D shallow water equations; semi-discrete central scheme; Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction Software:CWENO PDFBibTeX XMLCite \textit{J.-Z. Chen} and \textit{Z.-K. Shi}, J. Hydrodyn., Ser. B 18, No. 4, 436--442 (2006; Zbl 1203.76021) Full Text: DOI